Question

a financial analyst is examining the income distribution of employees in a large corporation. the analyst finds that the range of incomes is $80,000, the inter - quartile range (iqr) is $30,000, and the standard deviation is $20,000. based on these measures of spread, select two correct answers.

1. the majority of employees have incomes that deviate by $20,000 from the mean income.
2. the middle 50% of employees have incomes that vary by $30,000.
3. the highest income in the corporation is $80,000.
4. the standard deviation indicates that all employees have incomes within $20,000 of the mean.

Explanation:

Step1: Recall measure - spread concepts

The inter - quartile range (IQR) represents the middle 50% of the data. The standard deviation measures how much the data deviates from the mean.

Step2: Analyze each statement

• The standard deviation of $20,000 means that, on average, data points deviate from the mean by $20,000.
• The IQR of $30,000 means the middle 50% of employees have incomes that vary by $30,000.

Answer:

The middle 50% of employees have incomes that vary by $30,000; The standard deviation indicates that employees deviate by $20,000 from the mean income.